rename exercise to pythagorean-triplet

config.json

@@ -411,6 +411,23 @@
         "prerequisites": [],
         "difficulty": 2
       },
+      {
+        "slug": "pythagorean-triplet",
+        "name": "Pythagorean Triplet",
+        "uuid": "23992d00-d1e4-4ee3-9ca7-50885124d813",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4
+      },
+      {
+        "slug": "pythagorean-triplets",
+        "name": "Pythagorean Triplets",
+        "uuid": "630a11f5-e640-4e4d-af01-30f3bbcf495c",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 4,
+        "status": "deprecated"
+      },
       {
         "slug": "affine-cipher",
         "name": "Affine Cipher",
@@ -716,6 +733,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "bowling",
+        "name": "Bowling",
+        "uuid": "f6ca2cb9-f169-4c3e-8a64-6d3326b01d70",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 6
+      },
       {
         "slug": "bank-account",
         "name": "Bank Account",
@@ -767,22 +792,6 @@
         ],
         "prerequisites": [],
         "difficulty": 8
-      },
-      {
-        "slug": "bowling",
-        "name": "Bowling",
-        "uuid": "f6ca2cb9-f169-4c3e-8a64-6d3326b01d70",
-        "practices": [],
-        "prerequisites": [],
-        "difficulty": 6
-      },
-      {
-        "slug": "pythagorean-triplets",
-        "name": "Pythagorean Triplet",
-        "uuid": "630a11f5-e640-4e4d-af01-30f3bbcf495c",
-        "practices": [],
-        "prerequisites": [],
-        "difficulty": 4
       }
     ]
   },

exercises/practice/pythagorean-triplet/.docs/instructions.md

@@ -0,0 +1,23 @@
+# Description
+
+A Pythagorean triplet is a set of three natural numbers, {a, b, c}, for which,
+
+```text
+a² + b² = c²
+```
+
+and such that,
+
+```text
+a < b < c
+```
+
+For example,
+
+```text
+3² + 4² = 5².
+```
+
+Given an input integer N, find all Pythagorean triplets for which `a + b + c = N`.
+
+For example, with N = 1000, there is exactly one Pythagorean triplet for which `a + b + c = 1000`: `{200, 375, 425}`.

exercises/practice/pythagorean-triplet/.docs/introduction.md

@@ -0,0 +1,19 @@
+# Introduction
+
+You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles.
+One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project.
+The letter reads:
+
+> Dear Mathematician,
+>
+> I need your help.
+> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c².
+> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N.
+> Calculating these triplets by hand would take me years, but I hear you are more than up to the task.
+>
+> Time is of the essence.
+> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem.
+
+Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition.
+Your work could have far-reaching implications, unlocking new possibilities in science and engineering.
+Can you rise to the challenge and make history?

exercises/practice/pythagorean-triplet/.meta/config.json

@@ -0,0 +1,23 @@
+{
+  "authors": [
+    "blakelewis"
+  ],
+  "contributors": [
+    "SimaDovakin",
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "pythagorean-triplet.rkt"
+    ],
+    "test": [
+      "pythagorean-triplet-test.rkt"
+    ],
+    "example": [
+      ".meta/example.rkt"
+    ]
+  },
+  "blurb": "Given an integer N, find all Pythagorean triplets for which a + b + c = N.",
+  "source": "A variation of Problem 9 from Project Euler",
+  "source_url": "https://projecteuler.net/problem=9"
+}

exercises/practice/pythagorean-triplet/.meta/example.rkt

@@ -0,0 +1,24 @@
+#lang racket
+
+(provide triplets-with-sum)
+
+(define (primitives pmax)
+  (for*/list
+    ([m (in-naturals 2)]
+     #:break (> (* 2 (* m (add1 m))) pmax)
+     [n (in-range (add1 (remainder m 2)) m 2)]
+     #:when (= 1 (gcd m n)))
+    (define a (- (* m m) (* n n)))
+    (define b (* 2 (* m n)))
+    (define c (+ (* m m) (* n n)))
+    (sort (list a b c) < )))
+
+(define (triplets-with-sum p)
+  (define (scale-up triple)
+     (define perimeter (for/sum ([t triple]) t))
+     (cond
+       [(zero? (remainder p perimeter))
+         (define k (quotient p perimeter))
+         (for/list ([t triple]) (* k t))]
+       [else #f]))
+   (sort (filter-map scale-up (primitives p)) < #:key car))

exercises/practice/pythagorean-triplet/.meta/tests.toml

@@ -0,0 +1,31 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[a19de65d-35b8-4480-b1af-371d9541e706]
+description = "triplets whose sum is 12"
+
+[48b21332-0a3d-43b2-9a52-90b2a6e5c9f5]
+description = "triplets whose sum is 108"
+
+[dffc1266-418e-4daa-81af-54c3e95c3bb5]
+description = "triplets whose sum is 1000"
+
+[5f86a2d4-6383-4cce-93a5-e4489e79b186]
+description = "no matching triplets for 1001"
+
+[bf17ba80-1596-409a-bb13-343bdb3b2904]
+description = "returns all matching triplets"
+
+[9d8fb5d5-6c6f-42df-9f95-d3165963ac57]
+description = "several matching triplets"
+
+[f5be5734-8aa0-4bd1-99a2-02adcc4402b4]
+description = "triplets for large number"

exercises/practice/pythagorean-triplet/pythagorean-triplet-test.rkt

@@ -0,0 +1,38 @@
+#lang racket/base
+
+(require "pythagorean-triplet.rkt")
+
+(module+ test
+
+  (require rackunit rackunit/text-ui)
+
+  (define suite
+    (test-suite
+      "Return Pythagorean triplets with given perimeter"
+
+      (test-equal? "triplets whose sum is 12"
+        (triplets-with-sum 12) '((3 4 5)))
+
+      (test-equal? "triplets whose sum is 108"
+        (triplets-with-sum 108) '((27 36 45)))
+
+      (test-equal? "triplets whose sum is 1000"
+        (triplets-with-sum 1000) '((200 375 425)))
+
+      (test-equal? "no matching triplets for 1001"
+        (triplets-with-sum 1001) '())
+
+      (test-equal? "returns all matching triplets"
+        (triplets-with-sum 90) '((9 40 41) (15 36 39)))
+
+      (test-equal? "several matching triplets"
+        (triplets-with-sum 840)
+        '((40 399 401) (56 390 394) (105 360 375) (120 350 370)
+          (140 336 364) (168 315 357) (210 280 350) (240 252 348)))
+
+      (test-equal? "triplets for large number"
+        (triplets-with-sum 30000)
+        '((1200 14375 14425) (1875 14000 14125) (5000 12000 13000)
+          (6000 11250 12750) (7500 10000 12500)))))
+
+  (run-tests suite))

exercises/practice/pythagorean-triplet/pythagorean-triplet.rkt

@@ -0,0 +1,6 @@
+#lang racket
+
+(provide triplets-with-sum)
+
+(define (triplets-with-sum p)
+  (error "Please implement 'triplets-with-sum'"))